Watching cyclists struggle through the Tour de France from our armchairs (or should it be deckchairs?) is great fun, but as Burkard Polster and Marty Ross have discovered, it would be even more fun if the cyclists cycled in circles.

Cows kill 20 Americans every year. But you can halve your chance of dying of a heart attack by drinking 8 bottles of wine a week. Laugh in the face of death at the new comedy show with stand up mathematician Matt Parker and comedian Timandra Harkness...

"Mathematics is not yet ready for such problems." This is what the mathematician John Conway reportedly said about the Collatz conjecture, a simple-looking, yet unsolved mathematical mystery. This week Plus hosted two intrepid work experience students, Sabrina Qian and Joe Dickens, who decided to have a go at this fiendish problem nevertheless. And they made some intriguing discoveries. Here is what they came up with.

If you are (or were) an England fan and don't feel like watching Germany's unstoppable advance to take the ultimate trophy, why not use the freed-up time to look at the maths behind the beautiful game...